Method and system of three-dimensional positional finding

ABSTRACT

The present invention is an RF system and methods for finding a target T in three dimensional space configured to have a transponder disposed on the target T, a monitoring unit configured as a transceiver for determining or monitoring the location of the target T and an RF wireless communication system configured with a processor to repeatedly determine position, communication and other values between the transponder and monitoring unit and so as to generate a measured distance between units in three dimensional space by determining the measured distance of the target T by a spherical virtual triangulation relationship when successive values of said position information has a predetermined logical relationship relative to said previous values between said monitoring unit and transponder and/or slave unit disposed on the target T.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to radio frequency (RF) locatorsystems and techniques and, more particularly, to a method and system oftracking, locating and determining the location of people and/or objectsin three-dimensional space with a minimal or no fixed infrastructure.

2. Description of the Related Art

Most systems for locating a subject in three-dimensional space employthe use of heavy infrastructure such as a global positioning system todetermine the position of the object. However, such locating systems arecharacterized by shortcomings associated with the power requirements andexpensive infrastructure such as satellites that generate signals todetermine the position using four signals from separate sources. As aresult, such prior art methods and systems are not suitable to find,track and locate people and objects in a three-dimensional environmentwith minimal or no fixed infrastructure, for example, searching andfinding emergency workers in a three dimensional environment buildings,structures, terrain and other locations. The present inventionadvantageously provides location information in a three dimensionalenvironment without a large, expensive infrastructure.

Typical radio frequency RF systems do not have a reduced systeminfrastructure, which suffers from disadvantages including requirementsof setting up fixed RF reference points, antenna size, range and RFwavelength, whereby signal interference and degradation have limited thedevelopment of small power, compact RF systems to search, locate andtrack objects in three-dimensions. Such factors require additionaldevices and installation costs that have limited the deployment of RFlocation systems in a three-dimensional environment. As a result thereis a long-felt need for a three-dimensional system having reduced fixedreference points that can be produced at a lower cost. Reducing fixedreference points also has advantages of enabling a system to be deployedimmediately and quickly in multiple environments, including harshenvironments such as in fire and rescue operations without extensive setup and or installation requirements.

SUMMARY OF THE INVENTION Insert Final Versions of Broadest System andMethod Claims DESCRIPTION OF THE DRAWINGS

These and other advantages of the present invention are best understoodwith reference to the drawings, in which:

FIG. 1 is a diagram illustrating a method RF mobile tracking andlocating system where the operators and targets are rendered in threedimensional space as provided by an embodiment of the present invention;

FIG. 2 is a top view diagram illustrating RF mobile tracking andlocating system where the operators and targets are rendered in twodimensional space as provided in FIG. 1;

FIG. 3 is a block diagram illustrating RF mobile tracking and locatingsystem take into account a landscape profile;

FIG. 4 is a schematic diagram illustrating RF mobile tracking andlocating system to determine the position of the units using sphericalcoordinates; and

FIG. 5 is a schematic diagram illustrating a method of the tracking andlocating system to determine the position of the units using sphericalcoordinates.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1 there is shown a method and system for finding inthree-dimensional space. A system is established between a device and anobject and/or person and controlled by inputs related to positions ofthe device relative to the object. All operators of the device can bemobile. While numerous devices may be employed, each of at least threemaster devices as is described herein is necessary to accomplishlocating targets in three dimensional spaces.

According to the system of the present invention, the system can locatethe object or target T in three dimensional spaces. Master Units can beused to track, locate, and monitor persons and objects, each of which isequipped with a tag and/or Master Unit. The hardware components andsoftware can be integrated into a device or a module that can beattached or integrated with a proprietary device, PDA, GPS device,laptop, cell phone, two way radio and other existing devices (together,the resulting enabled unit will be referred to as the “device” or“Device”). The Devices can operate on any frequency from lowerfrequencies, including frequencies in the 100 mhz, 200 mhz, 400 mhz, 900mhz, 2.4 ghz frequencies. All operators of the Device can be mobile.Each mobile Device and slave also may have a compass, pedometer andaltimeter. Each master unit and tag has its own ID, and can includeadditional information such as data about the person or item that istagged. The information can also include data that can substitute theinformation that a compass, pedometer, and altimiter can provide. A baseunit broadcasts RF signals, which are returned by the tags. The tags canbe active tags (battery powered) or passive tags (powered by the baseunit or some other source). The master units identify the tagged objectand can graphically display location information, including bothdistance and direction, allowing the user to quickly and easily view theobjects being tracked or pass information to other devices that cancentralize the information.

A search process, which can be implemented by software, utilizes threeor more devices that can run the software. The software has the searchmethods that enable the Devices it runs on to find and locate otherdevices running the software. Devices can also be equipped with acompass, pedometer and altimeter device. Control software to search,find and locate the targets in three dimensional spaces. Methods aredisclosed to use the device to search, find and locate the object orperson in three dimensional spaces. A search process, which can beimplemented by software, utilizes three or more Devices that can run thesoftware that embodies the search methods described below.

According to various exemplary embodiments of the method of the presentinvention, a process to search, locate, and track targets is describedaccording to the following examples of finding techniques:

-   -   1. Three mobile operators tracking a target.    -   2. A combination of three of the group of stationary and mobile        operators:    -   3. All operators are mobile and are not equipped with pedometer        and/or altimeter:    -   4. All operators are Mobile and searching/tracking target inside        building:    -   5. A single searching/tracking mobile operator and three        stationary operators inside building or other three dimensional        environments:    -   6. A special case for a search/tracking mobile operator and two        stationary operators inside building:        In each of these exemplary embodiments control software can be        implemented as is detailed herein so as to implementation the        process for finding, locating, searching and tracking other        targets. An option that improves accuracy includes running        multiple techniques at the same time, sequentially (for example,        running two methods and averaging the results) or depending on        user preference or environment and, for example, complimentary        techniques that include virtual triangulation that is set forth        in U.S. Pub. No. 20050020279 A1; where the user would be able to        locate the tagged person or item once they reach the desired        floor. The use of more than three networked units will improve        accuracy. The networking can occur through multiple methods that        include fixed wire and wireless mesh networking, such as Zigbee.

Example (1) Of Three Dimensional Mobile Finding

As shown in FIG. 1, there is shown elements of users and devicecomponents searching, tracking and locating a target T. A systemprovided by an embodiment of the present invention for locating,monitoring and or tracking of targets (T) that can be animate orinanimate, or both. In this exemplary embodiment, each of the users oroperators can be mobile. Each of the users has a system utilizes one ormore of a compass, pedometer, and/or altimeter, or alternatively,another device, method or input that provides comparable information toeach unit. In this system, each of the units disposed on the targets tobe found and/or tracked also are equipped with altimeter or device toprovide such comparable information.

At least three users U_(a), U_(b), and U_(c) are initially positionedrandomly in three dimensional coordinate spaces relative to the target Tsuch as, for example, users U_(a), U_(b), and U_(c) are positionedrelative to North and East quadrants with the target at a heightrelative to each. It is appreciated that the position of target T can bedisplayed on a plane and its vertical coordinate value separately, forexample, as a number or circle, etc. Certain initial conditions areconfigured in this three dimensional coordinate space relative to thetarget T in a manner that is logical to the users U_(a), U_(b), andU_(c):

-   -   1. It is useful to establish a “natural” system of directional        coordinates on plain relative to the users such as North-South,        East-West, and a third coordinate relative to the height or        altitude of the target T, such as, for example, density        altitude, MSA or the height above the sea level as can be        measured by the altimeter.    -   2. Each of the tracked target(s) is equipped with a slave unit        transponder having an altimeter configured to generate signals        of altitude or some other device or method to provide comparable        altitude information.    -   3. Each of the master units used by the users U_(a), U_(b), and        U_(c) are equipped with altimeter, compass and pedometer or,        alternatively, the user has an alternative means of determining        the distanced the master unit travels, relative height and        direction.    -   4. An origin or starting point is calibrated relative to each of        the master units used by the users U_(a), U_(b), and U_(c) and        the origin coordinates are stored in the natural system of        coordinates so as to be known as an initial reference condition.    -   5. Each of the users U_(a), U_(b), and U_(c) having master units        are mobile, whereby each master unit of users U_(a), U_(b), or        U_(c) is capable of measuring or otherwise calculating and        storing a distance the master unit travels as well as the        direction or bearing of a user's U_(a), U_(b), or U_(c) movement        relatively to one axis of the configured natural system of        directional coordinates, for example, the North axis.

Now making reference to FIGS. 1 and 2, the users U_(a), U_(b), and U_(c)are represented as points in three dimensional coordinate space relativeto the target T, whereby the “North” axis is configured as a referenceaxis. The reference axis is useful to measure or calculate the target Tcoordinates and the bearing of a user's U_(a), U_(b), or U_(c) movementrelative to the “North” axis and the target T. Such measurementadvantageously can be calculated by projecting points of the user'sU_(a), U_(b), or U_(c) onto the natural plane relative to the target Tfrom the three dimensional coordinate space, thereby calculating thetarget T coordinates on such natural plane so as to determine thebearing of operator movement toward the target T such as, for example,relatively to the “North” axis.

According to a first mobile finding technique and method of the presentinvention, a user U_(a), U_(b), or U_(c) can be designated themonitoring Unit that is searching and/or tracking the target T in asearch operation. Advantageously, the present invention can beconfigured so that all users U_(a), U_(b), and U_(c) can be utilized asmonitoring units (Devices 1, 2 and 3 herein) according to anotherembodiment of the present invention. In the first mobile findingtechnique the target T is projected into the two dimensional naturalplane after the units disposed on users U_(a), U_(b), and U_(c) arenormalized. After normalization, which can be initiated at initial poweron or entering the finding mode, the mobile finding method precedesutilizing the following steps:

-   -   1. The master monitoring unit (device 1), in this example user        U_(a), periodically measures a distance R₁ relative to the        target T with reference to the North axis. As a safeguard for        further calculations, if the distance D to target T from the        user U_(a) exceeds a predetermined threshold “D”, the master        monitoring unit (device 1) can be configured to notify user        U_(a) to recalibrate and/or normalize and then begin again, for        example, at a zero height setting.    -   2. Master monitoring operator U_(a) enables (monitoring device        20) in a search/track mode and device 1 will transmit to other        two monitoring devices (device 2 and device 3) the unique RF        identification number of the target T being searched for and/or        tracked.    -   3. Monitoring devices 2 and 3 will determine the corresponding        distances to the target, i.e. R₂ and R₃, the height values of        users U_(b), and U_(c), having devices 2 and 3 disposed thereon,        the coordinates values (X₂₁, X₂₂), (X₃₁, X₃₂) projected on the        plane.    -   4. Master monitoring user U_(a) enables device 1 to send a        request to the slave unit disposed on target T for it to read        the altimeter value corresponding to the target's T height.    -   5. Slave unit disposed on target T transmits to device 1 of the        monitoring operator U_(a) a signal corresponding to the value of        the target “height” from the altimeter.    -   6. From such value, the target T and positions of users U_(a),        U_(b), and U_(c) are “projected” on the natural plane, whereby        all coordinates in a third dimension or height are made equal to        zero. This compression essentially creates radii R₁, R₂ and R₃        from devices 1, 2 and 3. From such radii R₁, R₂ and R₃ and such        corresponding height values of users U_(a), U_(b), and U_(c) and        target T the “projected” distances between each of users U_(a),        U_(b), and U_(c) and the target T and can be calculated, for        example, distance values R_(p1), R_(p2), and R_(p3) will be        calculated.    -   7. From user U_(a), U_(b), and/or U_(c) coordinates projected on        the plane having values (X₁₁, X₁₂), (X₂₁, X₂₂), (X₃₁, X₃₂) and        distance values R_(p1), R_(p2), and R_(p3) the target        coordinates (X₁, x₂) can be calculated or otherwise determined.    -   8. Master monitoring user's U_(a) device enables then calculates        a bearing toward the target T using a coordinate axis, for        example, relatively to “North” axis. Thereafter, the device 1        can prompt user's U_(a) with direction.    -   9. Master monitoring user U_(a) begins a new movement in a        particular direction. For an accurate determination of user        U_(a) coordinates, device 1 recalculates. For example, after        user U_(a) moves a certain distance such user's U_(a) (1) height        (the third coordinate) and (2) bearing or angle of movement        relatively to the “North” axis is determined to update the        coordinates of user U_(a) such as, for example, after every 1        meter of movement. Advantageously, such technique takes into        account any landscape profile as is set forth in FIG. 3 and the        Examples below.    -   10. During movement of user U_(a) device 1 can be configured to        process, compute or otherwise determine the difference between        user U_(a) projections in the coordinate natural plane. Device 1        can prompt user U_(a) when a predetermined distance is reached        (R), for example 10 meters.    -   11. At this point, the device 1 of master monitoring user U_(a)        can be configured to in the searching and/or tracking can notify        any other devices of its position, for example, devices 2 and 3,        whereby device 1 makes distance measurements and can send        requests to other devices 2 and device 3 to measure their        distances.    -   12. Upon receiving such request devices 2 and 3 perform distance        measurements to target T for (1) height and (2) position;        sending a value and coordinate data of coordinates values of        each of users U_(b), and U_(c) to device 1 of U_(a).    -   13. Device 1 of U_(a) repeats one or more of the steps of        process paragraphs 4-10 and thereafter prompts device 1 of U_(a)        for a new bearing angle.    -   14. Upon such prompt, U_(a) changes its direction of movement so        as to create another set of coordinate point as reference.    -   15. Steps 4-14 can be repeatedly or iteratively until the target        T is found or otherwise located.

Tracking Method According to First Finding Technique

According to another exemplary embodiment the method of the presentinvention, a process for searching in the natural two dimensional spaceis described, for example, after points are determined by projectingonto the plane. The projected points of the target T into the naturalplane will have coordinate values (X₁₁, X₁₂), (X₂₁, X₂₂), (X₃₁, X₃₂) anddistance values R_(p1), R_(p2), and R_(p3) with the target coordinates(X₁, X₂) are projected using the above procedures.

A profile tracking method modifies the procedures used in theabove-identified First Example of Three Dimensional Mobile Finding tocreate a process of searching/tracking in two-dimensional space. Thethird coordinate (height) is used to take into account the landscapeprofile as shown in FIG. 3. For example, if the user U_(a) movesdirectly from a place A to place B an altitude factor is introduced bythe terrain.

As is illustrated in FIG. 3, the actual distance d₁ traveled betweenplaces A and B is variable, as follows; a direct line between places ABis 10 meters, as is shown by broken line AB. Alternatively, a longerdistance d₂ is actually traveled along solid line AB between places Aand B. As a result, the length of the solid line AB is greater than thelength of the direct route broken line AB, which reflects the actualoperator travel and the landscape profile such as, for example, it islarger such as 15 meters. Thus, the accuracy of determining thecoordinates of point C will be impacted, unless the operator device willkeep updating coordinates every 1-meter, using the height measurements.

For example, in case of an obstacle or terrain so as to take the mostefficient path, the user U_(a) switches the monitoring or master unit tomanual control. The user U_(a) With help of compass determines the angleunder which he is going to move in order to bypass the obstacle. Theuser U_(a) moves along relatively straight lines and, prior to anydirection changes, The user U_(a) inputs via an input such as a buttonto the monitoring unit an angle as to the direction the user is going tobe moving (relative to the “North” axis) so as to enable the monitoringunit to compute or keep track of the user's U_(a) coordinates.

An exemplary method of to take the most efficient path around anobstacle or terrain can be described as follows to take advantage offollowing techniques that improve performance:

-   1. In case of an obstacle or terrain so as to take the most    efficient path, the user U_(a) switches the monitoring or master    unit to manual control. The user U_(a) with help of compass    determines the angle under which he is going to move in order to    bypass the obstacle. The user U_(a) moves along relatively straight    lines and, prior to any direction changes, The user U_(a) inputs via    an input such as a button to the monitoring unit an angle as to the    direction the user is going to be moving (relative to the “North”    axis) so as to enable the monitoring unit to compute or keep track    of the user's U_(a) coordinates.-   2. All users U_(a), U_(b) and or U_(c) are mobile. The following    steps can be taken with respect to user U_(a), but also similar    steps may be taken by users U_(b) and or U_(c) using their units,    for accurate determination of the unit's coordinates for U_(a). Once    user U_(a) has moved a certain distance, for example, after every    1-meter of operator movement, a determination is made of the user's    U_(a) height (the third coordinate) and the bearing (angle) of    movement relatively to the “North” axis. Corresponding updates are    made to the user's U_(a) coordinates in order to take into account    the landscape profile. In case of an obstacle the user U_(a)    switches the monitoring or master unit to manual control. The user    U_(a) With help of compass determines the angle under which he is    going to move in order to bypass the obstacle. The user U_(a) moves    along relatively straight lines and, prior to any direction changes,    The user U_(a) inputs via an input such as a button to the    monitoring unit an angle as to the direction the user is going to be    moving (relative to the “North” axis) so as to enable the monitoring    unit to compute or keep track of the user's U_(a) coordinates.-   3. The compass incorporated in the user's U_(a) monitoring or master    unit can determine the “North” direction. The user U_(a) can    determine a reference of to North from the unit or a display of    North on the unit. As a result, the user U_(a) can be given    instructions and display of all directions of movement (bearing)    relative to the “North” direction. For example, a command given to    user U_(a) of “45 degrees North-East” instructs the user U_(a)    facing North to go at a 45 degree angle to the right.-   4. When numerous users U_(a), U_(b), . . . U_(N) are searching for M    targets T_(a), T_(b) . . . T_(M), where (M<N), a similar search    method can be used as described herein, whereby the monitoring or    master unit of user U_(a) transmits a target ID to adjacent master    units of U_(b), . . . U_(N). In return the master unit of user U_(a)    receives the distances to the target T and coordinates of adjacent    master units of U_(b), . . . U_(N) that responded with the distance    measurements. Based on this information (target ID, distance and    coordinates) and the coordinates of the searching the master unit of    user U_(a) computes the position of target T.-   5. The searching method when numerous users U_(a), U_(b), . . .    U_(N) are searching for M targets T_(a), T_(b), . . . T_(M) can    utilize RF multi-channel technology to efficiently utilize the    bandwidth such as, for example, time division, frequency division,    etc. To further enhance the capabilities of the monitoring or master    units as well as the slave units disposed on the target(s) T,    whereby the units utilize different channels and time division    within the same channels to communicate with different units in real    time.

Example (2) Three Dimensional Finding Stationary and Mobile Operators

If users each or any of numerous users U_(a), U_(b), U_(c), U_(d) . . .U_(N) are searching for multiple M targets T_(a), T_(b), . . . T_(M);three dimensional finding can occur utilizing four stationary usersU_(a), U_(b), U_(c) and U_(d), whereby it is possible to determine allthree coordinates for every other user U_(e), . . . U_(N) that is mobileincluding a user system U_(M) disposed on the target T. In this example,each user U_(a), U_(b), U_(c) and U_(d) searching and or tracking atarget T_(M) or other multiple targets T_(a), T_(b), . . . T_(M) do notneed to utilize the pedometer and or altimeter; however, they will stillrequire use of an integrated compass or other device or method that canprovide equivalent information. Moreover, if users U_(a), U_(b), U_(c)and U_(d) searching and or tracking target T_(M) are stationary, forevery other users U_(e) . . . U_(N) searching and or tracking targetT_(M), the unit of the fifth user U_(e) or others U_(N) do not need tomeasure the traveled distance and height because the coordinates of thefifth or any other user U_(e) can be determined from the distancemeasurements and coordinates of stationary master units of each usersU_(a), U_(b), U_(c) and U_(d).

An exemplary method of the user utilizing the master and slave unitswhen users U_(a), U_(b), U_(c), . . . U_(N) are searching for M targetsT_(a), T_(b), . . . T_(M) and four users U_(a), U_(b), U_(c) and U_(d)are stationary, then it is possible to determine all three coordinatesfor every other mobile user U_(e), . . . U_(N) is as follows:

-   -   1. Establishing a system of coordinates on a natural plain that        is referenced to four parts of the world (North-South,        East-West).    -   2. At least one active master or monitoring unit of a user        U_(a), U_(b), U_(c), . . . U_(N) has a compass either configured        to generate directional information with reference to the        coordinate plane, i.e. North.    -   3. Obtain origin coordinates of stationary or known determined        from the distance measurements and coordinates of stationary        master units of each users U_(a), U_(b), U_(c) and U_(d) in the        natural coordinate system.    -   4. Each user U_(a), U_(b), U_(c) and U_(d) of stationary master        units are not disposed along one straight line and/or in the        plane such that different coordinate points can be obtained for        each user U_(a), U_(b), U_(c) and U_(d) of stationary master        units

The process of a search consists of the establishing the followingsteps:

-   -   1. Monitoring unit (device 5) of user U_(e) periodically        measures a distance R₅ to target T. If the distance R₅ to target        T exceeds a predetermined threshold “D”, monitoring unit        notifies user U_(e) of this condition.    -   2. Beginning of a search. Monitoring unit of user U_(e) is        enabled in a search/track mode and the Monitoring unit of user        U_(e) can transmit the RF id or other identification number        (code) of the target T to be searched for and/or tracked, to        four users U_(a), U_(b), U_(c) and U_(d) of the stationary        monitoring units (devices 1, 2, 3 and 4).    -   3. Stationary monitoring units (devices 1, 2, 3 and 4) of users        U_(a), U_(b), U_(c), and U_(d) determine respective distances        R₁, R₂, R₃ and R₄ to target T, and send these distances and the        coordinates of U_(a), U_(b), U_(c) and U_(d) to monitoring unit        (device 5) of user U_(e).    -   4. Stationary monitoring units (devices 1, 2, 3 and 4) of users        U_(a), U_(b), U_(c) and U_(d) determine the distances to the        searching/tracking to monitoring unit (device 5) of user U_(e)        (R_(1-Ua) (Ro1), R_(2-Ub) (Ro2), R_(3-Uc) (Ro3), and R_(4-Ud)        (Ro4)). The values of R_(Ua1), R_(Ub2), R_(Uc3) and R_(Ud4) are        transmitted or otherwise sent to monitoring unit (device 5) of        user U_(e).    -   5. Based on the transmitted supplied information of values the        monitoring unit (device 5) user U_(e) calculates coordinates        (X₁₅, X₂₅, X₃₅) of user U_(e) and coordinates (X₁₁, X₂₁, X₃₁),        (X₁₂, X₂₂, X₃₂), (X₁₃, X₂₃, X₃₃), (X₁₄, X₂₄, X₃₄) respectively        of stationary monitoring units (devices 1, 2, 3 and 4) of users        U_(a), U_(b), U_(c) and U_(d).    -   6. Device 5 (the monitoring unit of user U_(e)) calculates and        or otherwise determines coordinates (x₁, x₂, x₃) of target T        based on the supplied data R_(1-Ua), R_(2-Ub), R_(3-Uc) and        R_(4-Ud) and coordinates (X₁₁, X₂₁, X₃₁), (X₁₂, X₂₂, X₃₂), (X₁₃,        X₂₃, X₃₃), (X₁₄, X₂₄, X₃₄) of users U_(a), U_(b), U_(c) and        U_(d).    -   7. Using coordinates (x₁, x₂, x₃) of target T and known        coordinates (x₁, x₂, x₃) of monitoring unit (device 5) of user        U_(e), the device 5 calculates an angle of motion of device 5 of        user U_(e) toward the target T.    -   8. Device 5 displays compass information with an indication of        suggested direction of motion of user U_(e). Device 5 can        display an image of coordinate grid with the location of users        U_(a), U_(b), U_(c), . . . U_(N) and target T, for example, user        U_(e) and users U_(a), U_(b), U_(c) and U_(d) relative to target        T.    -   9. Device 5 and user U_(e) begin to travel in the indicated        direction.    -   10. Periodically, for example every 15 seconds (or every 10        meters), device 5 of user U_(e) repeats steps 1-10 so as to        provide to device 5 of user U_(e) correction of direction of        motion information on the device 5. Advantageously, during the        repeating of steps 1-10 device 5 of user U_(e) requests updates        from of stationary monitoring units (devices 1, 2, 3 and 4) of        users U_(a), U_(b), U_(c) and U_(d) so that new signals are        transmitted to device 5 and device 5 (the monitoring unit of        user U_(e)) calculates and or otherwise determines coordinates        (x₁, x₂, x₃) of target T.    -   11. Steps 1-10 are repeated until the monitoring unit of user        U_(e) finds target T.

The following defined terms are used throughout the process description:

R(i)—distance d of i-th operator to target T;

d—distance traveled (by a particular mobile user)

x₁—first coordinate target T

x₂—second coordinate target T

x₃—third coordinate target T

X₁(i)—first coordinate operator i

X₂(i)—second coordinate operator i

X₃(i)—third coordinate operator i

DA—Device action

P(i)—i-th standard computational procedure

RF ID code—target T identification code.

To determine the coordinates by calculating Procedure 1 of the target T;from sphere equations can calculate the position as follows:(x ₁ −X ₁₁)²+(x ₂ −X ₂₁)²+(x ₃ −X ₃₁)² =R ₁ ²  (1)(x ₁ −X ₁₂)²+(x ₂ −X ₂₂)²+(x ₃ −X ₃₂)² =R ₂ ²  (2)(x ₁ −X ₁₃)²+(x ₂ −X ₂₃)²+(x ₃ −X ₃₃)² =R ₃ ²  (3)(x ₁ −X ₁₄)²+(x ₂ −X ₂₄)²+(x ₃ −X ₃₄)² =R ₄ ²  (4)By removing the parentheses and subtracting equation (2) from equation(1) we can express x₂ through x₁ and x₃. By removing the parentheses andsubtracting equation (3) from equation (2) we can express x₃ through x₁when the obtained results of x₂ are substituted as x₁. Furthersubstitution in equation (1) of the obtained result of x₃, we can obtainthe dependency of x₂ from x₁. Further substitution in equation (1) ofthe obtained result of x₃ and the obtained results of x₂ we can obtainx₁. Finally we can obtain x₂ and x₃ by substituting the obtained resultsof values x₁ into x₂ from x₁ dependency and x₃ from x₁ dependency. As aresult of the substitutions and computations, eight points are obtainedso as to be used for consecutive substitutions in equation (4).

The set of coordinates for equation (4) that converts equation (4) intothe equality that will produce the desired points, as follows:(x ₁ =T,x ₂=(TN+O)/KF,x ₃=(L−MT)/K)(x ₁ =T,x ₂=(UN+O)/KF,x ₃=(L−MT)/K)(x ₁ =T,x ₂=(UN+O)/KF,x ₃=(L−MU)/K)(x ₁ =T,x ₂=(TN+O)/KF,x ₃=(L−MU)/K)(x ₁ =U,x ₂=(TN+O)/KF,x ₃=(L−MU)/K)(x ₁ =U,x ₂=(UN+O)/KF,x ₃=(L−MT)/K)(x ₁ =U,x ₂=(TN+O)/KF,x ₃=(L−MT)/K)(x ₁ =U,x ₂=(UN+O)/KF,x ₃=(L−MU)/K)where:T=(−R+sqrt(R²−4QS))/2QU=(−R−sqrt(R²−4QS)/2QQ=((KF)²+N²+(FM)²)R=((−2(X₁₁)(RF)²+2NO−2KF(X₂₁)N−2(F²)ML+2X(₃₁)(F²)KMS=(O²−2X(₂₁)KFO+(FL)2−2X(₃₁)L(F²)K+PP=((X₁₁)²+(X₂₁)²+(X₃₁)²−R₁ ²Q=((KF)²+N²+(FM)²)O=(KC−EL)N=(EM−KD)M=(HF−ID)K=(JF−IE)L=(FK−IC−FG)K=R₂ ²−R₃ ²J=2(X₃₃−X₃₂)I=2(X₂₃−X₂₂)H=2(X₁₃−X₁₂)F=2(X₂₂−X₂₁)E=2(X₃₂−X₃₁)D=2(X₁₂−X₁₁)G=((X₁₂)²+(X₂₂)²+(X₃₂)²−(X₁₃)²−(X₂₃)²−(X₃₃)²)C=B−AB=R₁ ²−R₂ ²A=((X₁₁)²+(X₂₁)²+(X₃₁)²−(X₁₂)²−(X₁₂)²−(X₃₂)²)

Similarly, To determine the coordinates by calculating Procedure 1 ofthe target T; from sphere equations can calculate the position asfollows:(X ₁₅ −X ₁₁)²+(X ₂₅ −X ₂₁)²+(X ₃₅ −X ₃₁)²=(R _(1-Ua))²  (5)(X ₁₅ −X ₁₂)²+(X ₂₅ −X ₂₂)²+(X ₃₅ −X ₂₃)²=(R _(2-Ub))²  (6)(X ₁₅ −X ₁₃)²+(X ₂₅ −X ₂₃)²+(X ₃₅ −X ₃₃)²=(R_(3-Uc))²  (7)(X ₁₅ −X ₁₄)²+(X ₂₅ −X ₂₄)²+(X ₃₅ −X ₃₄)²=(R_(4-Ud))²  (8)By removing the parenthesis and subtracting equation (6) from equation(5) we can express X₂₅ through X₁₅ and X₃₅. By removing the parenthesisand subtracting equation (7) from equation (6) we can express X₃₅through X₁₅ when the obtained results of X₂₅ are substituted through X₁₅and X₃₅. Further substitution in equation (5) of the obtained result ofX₃₅, we can obtain the dependency of X₂₅ from X₁₅. Further substitutionin equation (5) of the obtained result of X₃₅ and the obtained resultsof X₂₅ we can obtain X₁₅. Finally we can obtain X₂₅ and X₃₅ bysubstituting the obtained results of values X₁₅ into X₂₅ from X₁₅dependency and X₃₅ from X₁₅ dependency. As a result of the substitutionsand computations, eight points are obtained so as to be used forconsecutive substitutions in equation (8).

The set of coordinates for equation (8) turns the equation (8) intoequality that converts the desired points of the coordinates of userU_(e) of device 5, as follows:(X ₁₅ =T,X ₂₅=(TN+O)/KF,X ₃₅=(L−MT)/K)(X ₁₅ =T,X ₂₅=(UN+O)/KF,X ₃₅=(L−MT)/K)(X ₁₅ =T,X ₂₅=(UN+O)/KF,X ₃₅=(L−MU)/K)(X ₁₅ =T,X ₂₅=(TN+O)/KF,X ₃₅=(L−MU)/K)(X ₁₅ =U,X ₂₅=(TN+O)/KF,X ₃₅=(L−MU)/K)(X ₁₅ =U,X ₂₅=(UN+O)/KF,X ₃₅=(L−MT)/K)(X ₁₅ =U,X ₂₅=(TN+O)/KF,X ₃₅=(L−MT)/K)(X ₁₅ =U,X ₂₅=(UN+O)/KF,X ₃₅=(L−MU)/K)where:T=(−R+sqrt(R²−4QS))/2QU=(−R−sqrt(R²−4QS)/2QQ=((KF)²+N²+(FM)²)R=((−2(X₁₁)(RF)²+2NO−2KF(X₂₁)N−2(F²)ML+2X(₃₁)(F²)KMS=(O²−2X(₂₁)KFO+(FL)2−2X(₃₁)L(F²)K+PP=((X₁₁)²+(X₂₁)²+(X₃₁)²−R₁ ²Q=((KF)²+N²+(FM)²)O=(KC−EL)N=(EM−KD)M=(HF−ID)K=(JF−IE)L=(FK−IC−FG)K=Ro2²−Ro3²J=2(X₃₃−X₃₂)I=2(X₂₃−X₂₂)H=2(X₁₃−X₁₂)F=2(X₂₂−X₂₁)E=2(X₃₂−X₃₁)D=2(X₁₂−X₁₁)G=((X₁₂)²+(X₂₂)²+(X₃₂)²−(X₁₃)²−(X₂₃)²−(X₃₃)²)C=B−AB=R₁ ²−R₂ ²A=((X₁₁)²+(X₂₁)²+(X₃₁)²−(X₁₂)²−(X₁₂)²−(X₃₂)²)

An exemplary method of finding a direction of motion or angle A towardthe target T when users U_(a), U_(b), U_(c), . . . U_(N) are searchingfor M targets T_(a), T_(b), . . . T_(M) utilizing the master and slaveunits. Simply, the method and system of the present invention candetermine a direction of motion of user U_(e) of device 5 toward thetarget T. For Procedure 3: calculation of direction of motion or angle Aof device 5 used by user U_(e) in motion toward target T can bedetermined relative to the natural coordinates system “North” axis.Angle A is calculated based on the mobile user U_(e) (device 5) andtarget T coordinates as follows:cos(A)=(x ₂ −X ₂₍₅₎)/R ₅  (9)therefore,A=arcos((x ₂ −X ₂₍₅₎)/R ₅)  (10)

A direction of motion of user U_(e) of device 5 can be calculated byusing the following steps:

-   -   1. If Angle A>90 & x₁<X1(5) then device 5 instructs and or        displays “(180-A) degrees in South-West” direction to user        U_(e).    -   2. If Angle A>90 & x₁>X₁₍₅₎ then device 5 instructs and or        displays “(180-A) degrees in South-East” direction to user        U_(e).    -   3. If Angle A<90 & x₁<X₁₍₅₎ then device 5 instructs and or        displays “A degrees in North-West” direction to user U_(e).    -   4. If Angle A<90 & x₁>X₁₍₅₎ then device 5 instructs and or        displays “A degrees in North-East” direction to user U_(e).

An exemplary method to search or track the direction of motion of device5 of user U_(e) using the system of the present invention, is furtherdefined as comprising:

-   -   1. If the distance R₅ to target T exceeds a predetermined        threshold “D”, R₅>D, then monitoring unit notifies user U_(e) of        this condition by displaying <<Search mode>> else <<Monitoring        mode>> (where D—distance threshold).    -   2. Otherwise, the monitoring unit notifies user U_(e) that        <<Search mode>> is ON.    -   3. Device action DA: Device 5 of user U_(e) sends the target ID        code to four stationary monitoring units (devices 1, 2, 3 and 4)        to four stationary users U_(a), U_(b), U_(c) and U_(d),        respectively    -   4. Device action DA: Devices 1, 2, 3 and 4 of the four        stationary users U_(a), U_(b), U_(c) and U_(d), respectively,        receive the target ID code and:        -   a. Perform a distance measurement to target that was            identified in (3);        -   b. Send back to device 5 of user U_(e) the measured distance            R_((i)) values (where i is 1-4) of devices 1, 2, 3 and 4 of            the four stationary users U_(a), U_(b), U_(c) and U_(d) to            the target T, and coordinate values (X₁₁, X₂₁, X₃₁), (X₁₂,            X₂₂, X₃₂), (X₁₃, X₂₃, X₃₃), (X₁₄, X₂₄, X₃₄).        -   c. Send back to Device 5 of user U_(e) measured distances            R_(o(i)) values, where i is the identity code of devices            1-4.    -   5. Device action DA: Device 5 of user U_(e) sends the target ID        code:        -   a. Based on the above information, using P₁ the device            calculates its own coordinate values (X₁₅, X₂₅, X₃₅).        -   b. Based on the above information, using P₂ the device            calculates the target coordinates: (X₁₅, X₂₅, X₃₅).        -   c. Based on (X₁₅, X₂₅, X₃₅), (x₁, x₂, x₃) values using P₃            the device determines angle A value and the direction of            motion toward the target relatively to the “North” axis.    -   6. Device 5 of user U_(e) stores angle A value and direction of        motion toward target T.    -   7. Device 5 of displays prompts user U_(e) with a suggested        motion direction toward the target.    -   8. User U_(e) moves with device 5 according to the recommended        direction, for example, for 15 seconds or other update interval.    -   9. Device action DA: Device 5 prompts user U_(e) to stop or        other update interval while he remains in motion.    -   10. Device action DA: Device 5 repeats paragraph 3-10 until        target is found.

Example (3) Three Dimensional Mobile Finding i. All Mobile Operators

According to yet another exemplary example of the method of the presentinvention, if all four users U_(a), U_(b), U_(c) and U_(d) are mobileand the fifth mobile user U_(e) is searching and/or tracking the targetT, then all four devices 1, 2, 3 and 4 disposed on users U_(a), U_(b),U_(c) and U_(d), respectively, are configured with a pedometer,altimeter and compass or, alternatively, some other device or method forproviding such comparable information. Device 5 of the fifth mobile userU_(e) is configured with a compass; as it is not necessary that device 5be equipped with a pedometer and/or altimeter and the method can beimplemented without them. According to the method of finding of thepresent invention, the methods embodied in the Second Example of ThreeDimensional Mobile Finding Stationary and Mobile Operator can beutilized to provide device 5 of the fifth mobile user U_(e) with adirection toward the target T when performing a searching and/ortracking process according to the present invention.

According to still yet another exemplary example of the method of thepresent invention, if all four users U_(a), U_(b), U_(c) and U_(d) aremobile and the fifth mobile user U_(e) is searching and/or tracking thetarget T, then all four devices 1, 2, 3 and 4 disposed on users U_(a),U_(b), U_(c) and U_(d), respectively, are configured with a compass butnot a pedometer and/or altimeter. Again, device 5 of the fifth mobileuser U_(e) is configured with a compass; as it is not necessary thatdevice 5 be equipped with a pedometer and/or altimeter. According to themethod of finding of the present invention, the methods embodied in theSecond Example of Three Dimensional Mobile Finding Stationary and MobileOperator can be utilized to provide device 5 of the fifth mobile userU_(e) with a direction toward the target T when performing a searchingand/or tracking process; however, the performance of the finding isdiminished as the condition must exist where one of users is moving theother users must remain stationary. For example, if only a compass isdisposed on the devices 1, 2, 3 and 4, then only user U_(a) is mobile,then users U_(b), U_(c) and U_(d) must be stationary while the fifthmobile user U_(e) is searching and/or tracking the target T.

According to a further exemplary example of the method of the presentinvention where all four users U_(a), U_(b), U_(c) and U_(d) are mobileand searching and or tracking a target T inside a building, then allfour devices 1, 2, 3 and 4 disposed on users U_(a), U_(b), U_(c) andU_(d), respectively, are configured with a pedometer and altimeter;however, a compass is optional. According to the process of the presentinvention, at least four devices 1, 2, 3 and 4 disposed on users U_(a),U_(b), U_(c) and U_(d), respectively, and configured with a pedometerand altimeter are necessary to accomplish the finding. According to themethod of finding of the present invention, the exemplary methodembodied in the Example (2) for Three Dimensional Mobile FindingStationary and Mobile Operator can be utilized, for example, informationis provided to and from device 4 of the fourth mobile user U_(d) with adirection toward the target T when performing a searching and/ortracking process.

Essentially, the process of the present invention is configured tosearch and/or track the target T without the need for creatingstationary devices 1, 2, 3 and 4 disposed on users U_(a), U_(b), U_(c)and U_(d). For example, four devices 1, 2, 3 and 4 disposed on usersU_(a), U_(b), U_(c) and U_(d) can search numerous targets T as well asfor tracking each of the devices 1, 2, 3 and 4 disposed on users U_(a),U_(b), U_(c) and U_(d) as targets T in the building, harsh environmentor uneven terrain. The process utilizes the input of a compass andpedometer as well as the knowledge of the origin coordinates of each ofthe devices 1, 2, 3 and 4 disposed on users U_(a), U_(b), U_(c) andU_(d) so as to determine and calculate the coordinates of each of thedevices 1, 2, 3 and 4. As a result, it is not necessary to hold the eachof the devices 1, 2, 3 and 4 fixed or stationary. The process furtherrelies on a third coordinate value of the operators in each of thedevices 1, 2, 3 and 4 disposed on users U_(a), U_(b), U_(c) and U_(d).This can be done by the use of altimeters, measurements of height offloors within buildings or other sources that provide information thatcan provide the height of the users.

The process of a search consists of the establishing the followingsteps:

-   -   1. Each of the mobile devices 1, 2, 3 and 4 disposed on users        U_(a), U_(b), U_(c) and U_(d) are employed and configured to        search and/or track a target T in the building. Each of the        mobile devices 1, 2, 3 and 4 disposed on users U_(a), U_(b),        U_(c) and U_(d) are configured with a compass and pedometers.        Again use of altimeters is optional.    -   2. Each of the mobile devices 1, 2, 3 and 4 disposed on users        U_(a), U_(b), U_(c) and U_(d) establishes a system of        coordinates in a plane that is referenced to a coordinate        system, for example, four parts of the world (North-South,        East-West).    -   3. The process takes into account a value for distance between        floors (floor height) that is known, measured initially or        otherwise estimated. Each of the mobile devices 1, 2, 3 and 4        disposed on users U_(a), U_(b), U_(c) and U_(d) is configured to        correlate the height value with the floor number and vise versa.    -   4. Each of the mobile devices 1, 2, 3 and 4 disposed on users        U_(a), U_(b), U_(c) and U_(d) exchange origin coordinates of all        users U_(a), U_(b), U_(c) and U_(d) in the a natural coordinate        system such that these are known.    -   5. Each of the mobile devices 1, 2, 3 and 4 disposed on users        U_(a), U_(b), U_(c) and U_(d) is configured to determine and/or        calculate a distance traveled by the operator as well as the        operator's direction of motion relatively to one of the axis of        the natural system of coordinates, for example “North” axis.    -   6. In an optional step, each of the mobile devices 1, 2, 3 and 4        disposed on users U_(a), U_(b), U_(c) and U_(d) is configured to        ignore or not account for distance measurement errors in order        to speed accuracy.    -   7. In yet another optional step, it is assumed that device 4 of        user U_(d) is the monitoring and or master unit performing the        searching/tracking of the target T. A default value can be        established by the process that device 4 of user U_(d) resides        on the floor that is closest to the target's T floor.

8. All of the mobile devices 1, 2, 3 and 4 disposed on users U_(a),U_(b), U_(c) and U_(d) operators are configured to display and/ortransmit a value corresponding to a floor upon which they reside.

The following defined terms are used throughout the process description:

R(i)—distance of i-th operator to target

d—distance traveled (by a particular mobile user);

x₁—first coordinate target T

x₂—second coordinate target T

x₃—third coordinate target T

X₁(i)—first coordinate operator i

X₂(i)—second coordinate operator i

X₃(i)—third coordinate operator i

DA—Device action

P(i)—i-th standard computational procedure

RF ID code—target T identification code.

To determine the coordinates by calculating Procedure 1 of the target T;from sphere equations can calculate the position as follows:(x ₁ −X ₁₁)²+(x ₂ −X ₂₁)²+(x ₃ −X ₃₁)² =R ₁ ²  (1)(x ₁ −X ₁₂)²+(x ₂ −X ₂₂)²+(x ₃ −X ₃₂)² =R ₂ ²  (2)(x ₁ −X ₁₃)²+(x ₂ −X ₂₃)²+(x ₃ −X ₃₃)² =R ₃ ²  (3)(x ₁ −X ₁₄)²+(x ₂ −X ₂₄)²+(x ₃ −X ₃₄)² =R ₄ ²  (4)By removing the parentheses and subtracting equation (2) from equation(1) we can express x₂ through x₁ and x₃. By removing the parentheses andsubtracting equation (3) from equation (2) we can express x₃ through x₁when the obtained results of x₂ are substituted as x₁. Furthersubstitution in equation (1) of the obtained result of x₃, we can obtainthe dependency of x₂ from x₁. Further substitution in equation (1) ofthe obtained result of x₃ and the obtained results of x₂ we can obtainx₁. Finally we can obtain x₂ and x₃ by substituting the obtained resultsof values x₁ into x₂ from x₁ dependency and x₃ from x₁ dependency. As aresult of the substitutions and computations, eight points are obtainedso as to be used for consecutive substitutions in equation (4).

The set of coordinates for equation (4) converts to the desired points,as follows:(x ₁ =T,x ₂=(TN+O)/KF,x ₃=(L−MT)/K)(x ₁ =T,x ₂=(UN+O)/KF,x ₃=(L−MT)/K)(x ₁ =T,x ₂=(UN+O)/KF,x ₃=(L−MU)/K)(x ₁ =T,x ₂=(TN+O)/KF,x ₃=(L−MU)/K)(x ₁ =U,x ₂=(TN+O)/KF,x ₃=(L−MU)/K)(x ₁ =U,x ₂=(UN+O)/KF,x ₃=(L−MT)/K)(x ₁ =U,x ₂=(TN+O)/KF,x ₃=(L−MT)/K)(x ₁ =U,x ₂=(UN+O)/KF,x ₃=(L−MU)/K)where:T=(−R+sqrt(R²−4QS))/2QU=(−R−sqrt(R²−4QS)/2QQ=((KF)²+N²+(FM)²)R=((−2(X₁₁)(RF)²+2NO−2KF(X₂₁)N−2(F²)ML+2X(₃₁)(F²)KMS=(O²−2X(₂₁)KFO+(FL)2−2X(₃₁)L(F²)K+PP=((X₁₁)²+(X₂₁)²+(X₃₁)²−R₁ ²Q=((KF)²+N²+(FM)²)O=(KC−EL)N=(EM−KD)M=(HF−ID)K=(JF−IE)L=(FK−IC−FG)K=R₂ ²−R₃ ²J=2(X₃₃−X₃₂)I=2(X₂₃−X₂₂)H=2(X₁₃−X₁₂)F=2(X₂₂−X₂₁)E=2(X₃₂−X₃₁)D=2(X₁₂−X₁₁)G=((X₁₂)²+(X₂₂)²+(X₃₂)²−(X₁₃)²−(X₂₃)²−(X₃₃)²)C=B−AB=R₁ ²−R₂ ²A=((X₁₁)²+(X₂₁)²+(X₃₁)²−(X₁₂)²−(X₁₂)²−(X₃₂)²)

Calculation of direction of motion or angle A of operator of device usedby user U_(d) in motion toward target T can be determined relative tothe natural coordinates system “North” axis. Angle A is calculated basedon the mobile user U_(d) device 4 and target T coordinates as follows:cos(A)=(x ₂ −X ₂₍₄₎)/R ₄  (9)therefore,A=arcos((x ₂ −X ₂₍₄₎)/R ₄)  (10)

ii. Spherical Virtual Triangulation

In order to determine the coordinate position P₁ and position P₂ of thetarget T, sphere equations can calculate the position according to thediscussion herein with reference to equations (1) through (8) so as toobtain a set of eight coordinates for equation (8).

Referring to FIG. 4, the present invention can utilize a method andprocess utilizing points on a sphere. For example, three spheres can beestablished with the centers that do not lie on a straight line usingdevices 1, 2 and 3 disposed on users U_(a), U_(b) and U_(c). As aresult, the number of useful points are found at the intersection ofsuch intersecting spheres, for example, the intersecting points of equaleither to zero, one, or two. Moreover, if the number of points is equalto two, then any such two points are located on the different sides ofplane passing through the centers of spheres.

Under certain conditions, the process of the present inventiondetermines the floor of the target T and the fourth operatorunambiguously. For example, we locate three stationary devices 1, 2 and3 disposed on users U_(a), U_(b) and U_(c) are located in the corners ofthe building and apply the constraints of procedure P₁, eithercoordinates of target T or coordinates of device 4 disposed on userU_(d) can be found for the spheres equations in P₁.

Three spheres with the centers, which do not lie on one straight, have anumber of points. The points lie at the intersection of these spheresand are equal either to zero, one, or two. If the number of points isequal to two, then both points are located on the different sides ofplane passing through the centers of spheres. Therefore optimal resultscan be obtained by arranging three devices, for example, devices 1, 2and 3 disposed on the users U_(a), U_(b) and U_(c), along the angles ofthe building, whereby the entire building is located inside theparallelepiped formed by the users U_(a), U_(b) and U_(c).

A method of using sphere equations formed by devices 1, 2 and 3 disposedon the users U_(a), U_(b) and U_(c) according to the present inventionis disclosed. Spheres can be formed from the signals of device 1disposed on user U_(a) that has a distance of R₁. Another sphere can beformed around device 2 disposed on user U_(b) that has a distance of R₂.Referring to FIG. 4, a circle is formed at the intersection of spheresformed around devices 1 and 2 having a center on the axis thatconnecting users U_(a) and U_(b) and the circle is perpendicular to thisaxis. The distances R₁, R₂, R₃ from to the target T from devices 1, 2and 3 disposed on users U_(a), U_(b) and U_(c) locate the target T_(ar)is located on this circle. Moreover, the sphere with a radius of R₃around user U_(c) intersects the circle only at one point.

Similarly, a direction of motion of user U_(d) of device 4 can becalculated by using the following steps:

-   -   1. If Angle A>90 & x₁<X₁₍₄₎ then device 4 instructs and or        displays “(180-A) degrees in South-West” direction to user        U_(d).    -   2. If Angle A>90 & x₁>X₁₍₄₎ then device 4 instructs and or        displays “(180-A) degrees in South-East” direction to user        U_(d).    -   3. If Angle A<90 & x₁<X₁₍₄₎ then device 4 instructs and or        displays “A degrees in North-West” direction to user U_(d).    -   4. If Angle A<90 & x₁>X₁₍₄₎ then device 4 instructs and or        displays “[A] degrees in North-East” direction to user U_(d).

In order to determine the coordinate position P₃ of the target T, sphereequations can calculate the position according to the discussion hereinwith reference to appropriate equations (1)-(10) above Coordinatescalculations according to equations (11), (12), (13) and (14) can beused to update the coordinates. For example, four coordinate pairs arepossible according to equations (11), (12), (13) and (14) according tothe number of possible directions of movement, for example, if AngleA>90 & x₁>X₁₍₄₎; Angle A>90 & x₁>X₁₍₄₎; Angle A<90 & x₁>X₁₍₄₎; and AngleA<90 & x₁>X₁₍₄₎ as set forth above. Accordingly, for every possibledirection of movement enumerated above, coordinates calculationsaccording to equations (11), (12), (13) and (14) can be used todetermine the coordinates of mobile devices 1, 2, 3 and 4 disposed onusers U_(a), U_(b), U_(c) and U_(d) after the passage of distance d inthe suggested direction displayed on the devices 1-4.X _(1(i))new=X _(1(i))−sin(A)*d,X _(2(i))new=X _(2(i))−cos(A)*d  (11)X _(1(i))new=X _(1(i))+sin(A)*d,X _(2(i))new=X _(2(i))−cos(A)*d  (12)X _(1(i))new=X _(1(i))−sin(A)*d,X _(2(i))new=X _(2(i))+cos(A)*d  (13)X _(1(i))new=X _(1(i))+sin(A)*d,X _(2(i))new=X _(2(i))+cos(A)*d  (14)

The process of a search consists of the establishing the followingsteps:

-   1. If the distance R₄ to target T exceeds a predetermined threshold    “D”, R₄>D, then monitoring unit notifies user U_(d) of this    condition by displaying <<Search mode>> else <<Monitoring mode>>    (where D—distance threshold).-   2. Otherwise, the monitoring unit notifies user U_(d) that <<Search    mode>> is ON.-   3. Device action DA: Device 4 stores the target ID code to itself    (device 4 of user U_(d)) and sends the target ID code to three    stationary monitoring units devices 1, 2, and 3 of users U_(a),    U_(b) and U_(c), respectively.-   4. DA of Devices 1, 2, and 3 of users U_(a), U_(b) and U_(c):    -   a) Device action DA: Devices perform a distance measurement to        target T identified by device 4 of user U_(d) in step (3) so as        to determine distances to the target R₁, R₂, and R₃.    -   b) Device action DA: Devices 1, 2, and 3 of users U_(a), U_(b)        and U_(c) transmit or otherwise send back to device 4 of user        U_(d) measured distances to the target R₁, R₂, and R₃, which can        be represented as distance R(i) values, where i is 1-3 having        coordinates values (X₁₁, X₂₁, X₃₁), (X₁₂, X₂₂, X₃₂), (X₁₃, X₂₃,        X₃₃).-   5. Device action DA: Device 4 calculates the target coordinates:    (x₁, x₂, x₃) using P₁ and location of Target T.    -   a) Using P₁ the device 4 calculates the target coordinates: (x₁,        x₂, x₃), which is based on the above information: R₁, R₂, R₃ and        R₄ the coordinates of mobile devices 1, 2, 3 and 4 disposed on        users U_(a), U_(b), U_(c) and U_(d) (X₁₁, X₂₁, X₃₁), (X₁₂, X₂₂,        X₃₂), (X₁₃, X₂₃, X₃₃) (X₁₄, X₂₄, X₃₄).    -   b) Based on target coordinate x₃ value, the device of device 4        determines the floor location of the target T.-   6. User U_(d) and device 4 can then proceed to another location such    as, for example, to the nearest elevator or stairs. At the same    time, device 4 determines the direction of user U_(d) movement or    angle A relative to coordinate axis “North”. If it is necessary to    change the direction of motion, device 4 of user U_(d) calculates    the traveled distance values from pedometer or other methods that    calculate distance traveled or computational data received from    devices 1, 2, and 3 of users U_(a), U_(b) and U_(c) that transmit or    otherwise send back to device 4 updated measured distances to the    target R₁, R₂, and R₃. User U_(d) either enters this value into    device 4 or and device 4 automatically calculates this distance    based on user U_(d) request. Thereafter, user U_(d) manually enters    into device 4 the new direction of motion and user U_(d) continues    to move. From the measured value of traveled distance and angle A,    the user's U_(d) motion relative to axis “North” the of device 4,    new coordinate pairs can be determined according to equations (11),    (12), (13) and (14) using procedure P₃.-   7. As user U_(d) reaches the elevator or stairs, user U_(d) can    prompt device 4 to store coordinates before moving in a vertical    direction.-   8. For example, a floor number can be manually entered. As user    U_(d) moves vertically to a desired location or floor where target T    is located, user U_(d) can enter the floor number into device 4 so    as to allow for user U_(d) device 4 with coordinate values (X₁₄,    X₂₄, X₃₄+height between origin floor and end floor). Alternatively,    other methods of determining the floor number can be utilized.-   9. All the while, the other users U_(a), U_(b) and U_(c) are also    free to move in the building. As each of the other users U_(a),    U_(b) and U_(c) move, they can enter and update coordinate values of    devices 1, 2 and 3, respectively, according to any one of steps 6    through 8 above. Advantageously, such continuous updating allows    devices 1, 2 and 3 of users U_(a), U_(b) and U_(c), respectively, to    determine and calculate new coordinate pairs according to equations    (11), (12), (13) and (14) using procedure P₃.-   10. When user U_(d) reaches a desired floor, part of step 3 is    repeated where U_(d) sends to the three/four stationary the targets    ID code.-   11. When any of users U_(a), U_(b) and/or U_(c) reaches a desired    floor, step 4 is repeated.-   12. When all users U_(a), U_(b), U_(c) and U_(d) reach the desired    floor, user U_(d) repeats step 5.-   13. Based on the (x₁, x₂, x₃) and (X₁₄, X₂₄, X₃₄) coordinate values    of the target T and user U_(d), device 4 can further determine the    direction of motion toward the target A (angle A) using the process    to determine P₂ as described above.-   14. If there is an obstacle as user U_(d) moves in a given    direction, device 4 of user U_(d) can process the obstacle if user    U_(d) follows the process, according to any one of steps 6 through 7    above. Also, if user U_(d) moves only along straight lines and prior    to any direction changes user U_(d) inputs into device 4 the an    angle under which user U_(d) is moving relative to the “North” axis.    In this manner, device 4 can calculate and store the user U_(d)    current coordinates.-   15. User U_(d) can repeat steps 3-14 until target T is found.

Example (5) Three Dimensional Mobile Finding A Single Mobile User andThree Stationary Users Inside a Building

According to another exemplary example of the method of the presentinvention where a user U_(a) having device 4 is mobile and searching andor tracking a target T inside a building. The devices 4 is configuredwith a compass however, a pedometer and altimeter is optional. Moreover,if devices 4 is configured without an altimeter, the search and/ortracking process is configured to rely on three stationary devices 1, 2and 3 as disposed on users U_(b), U_(c) and U_(d), respectively.

In order to determine the coordinates position of the target T, thefollowing conditions must be satisfied:

-   1. Each of the mobile devices 1, 2, 3 and 4 disposed on users U_(a),    U_(b), U_(c) and U_(d) establishes a system of coordinates in a    plane that is referenced to a coordinate system, for example, four    parts of the world (North-South, East-West).-   2. The dimensions of the building: Height=A; length=B and width=W    are known.-   3. Stationary devices 1, 2 and 3 as disposed on users U_(b), U_(c)    and U_(d), respectively are positioned in such way that the building    itself would be completely located inside the parallelepiped that is    formed by users U_(b), U_(c) and U_(d). For example, users U_(b),    U_(c) and U_(d) are arranged as following: (1) the dimensions of the    building located on one side of the plane passing through users    U_(b), U_(c) and U_(d) and (2) devices 1, 2 and 3 are not arranged    on a straight line disposed on users U_(b), U_(c) and U_(d). In    another example, if the shape of the building is a convex    polyhedron, users U_(b), U_(c) and U_(d) can be locate on any of the    faces or planes. A convex polyhedron can be defined algebraically as    the set of solutions to a system of linear inequalities:    mx<b  (15)-    where m is a real (s x 3) matrix and b is a real s-vector.-    However, users U_(b), U_(c) and U_(d) can move from one face or    plane to another as long as all three users U_(b), U_(c) and U_(d)    are switching faces or planes at the same time. For example, user    U_(b) planar coordinates are (0, 0, 0); user U_(c) planar    coordinates are (0, B, 0); and user U_(d) planar coordinates are (W,    B, A).-   4. After the floor height is established, each device 1, 2, 3 and 4    can calculate the floor height, number of floors, and floor number.-   5. Each device 1, 2, 3 and 4 for purposes of this example do not    account for distance measurement errors advantageously to improve    the speed of locating the target T.-   6. User U_(a) having device 4 is mobile or otherwise is the fourth    user that is charged with searching and or tracking a target T    inside a building. The devices 4 is configured with a compass    however, a pedometer and altimeter is optional.

The following defined terms are used throughout the process description:

R(i)—distance of i-th operator to target,

d—distance traveled (by a particular mobile user);

x₁—first coordinate target T

x₂—second coordinate target T

x₃—third coordinate target T

X₁(i)—first coordinate operator i

X₂(i)—second coordinate operator i

X₃(i)—third coordinate operator i

DA—Device action

P(i)—i-th standard computational procedure

RF ID code—target T identification code.

Procedure 1: To determine the coordinates of the target T; using sphereequations can calculate the position as follows:(x ₁ −X ₁₁)²+(x ₂ −X ₂₁)²+(x ₃ −X ₃₁)² =R ₁ ²  (1)(x ₁ −X ₁₂)²+(x ₂ −X ₂₂)²+(x ₃ −X ₃₂)² =R ₂ ²  (2)(x ₁ −X ₁₃)²+(x ₂ −X ₂₃)²+(x ₃ −X ₃₃)² =R ₃ ²  (3)By removing the parentheses and subtracting equation (2) from equation(1) we can express x₂ through x₁ and x₃. By removing the parentheses andsubtracting equation (3) from equation (2) we can express x₃ through x₁when the obtained results of x₂ are substituted as x₁. Furthersubstitution in equation (1) of the obtained result of x₃, we can obtainthe dependency of x₂ from x₁. Further substitution in equation (1) ofthe obtained result of x₃ and the obtained results of x₂ we can obtainx₁. Finally we can obtain x₂ and x₃ by substituting the obtained resultsof values x₁ into x₂ from x₁ dependency and x₃ from x₁ dependency. Weuse these points for consecutive substituions in the equation (3). Thedesired point set of coordinates must satisfy the following conditions:x₁<B, x₂<W, x₃<A, i.e. the target is inside the building.(x ₁ =T,x ₂=(TN+O)/KF,x ₃=(L−MT)/K)(x ₁ =T,x ₂=(UN+O)/KF,x ₃=(L−MT)/K)(x ₁ =T,x ₂=(UN+O)/KF,x ₃=(L−MU)/K)(x ₁ =T,x ₂=(TN+O)/KF,x ₃=(L−MU)/K)(x ₁ =U,x ₂=(TN+O)/KF,x ₃=(L−MU)/K)(x ₁ =U,x ₂=(UN+O)/KF,x ₃=(L−MT)/K)(x ₁ =U,x ₂=(TN+O)/KF,x ₃=(L−MT)/K)(x ₁ =U,x ₂=(UN+O)/KF,x ₃=(L−MU)/K)where:T=(−R+sqrt(R²−4QS))/2QU=(−R−sqrt(R²−4QS)/2QQ=((KF)²+N²+(FM)²)R=((−2(X₁₁)(RF)²+2NO−2KF(X₂₁)N−2(F²)ML+2X(₃₁)(F²)KMS=(O²−2X(₂₁)KFO+(FL)2−2X(₃₁)L(F²)K+PP=((X₁₁)²+(X₂₁)²+(X₃₁)²−R₁ ²Q=((KF)²+N²+(FM)²)O=(KC−EL)N=(EM−KD)M=(HF−ID)K=(JF−IE)L=(FK−IC−FG)K=R₂ ²−R₃ ²J=2(X₃₃−X₃₂)I=2(X₂₃−X₂₂)H=2(X₁₃−X₁₂)F=2(X₂₂−X₂₁)E=2(X₃₂−X₃₁)D=2(X₁₂−X₁₁)G=((X₁₂)²+(X₂₂)²+(X₃₂)²−(X₁₃)²−(X₂₃)²−(X₃₃)²)C=B−AB=R₁ ²−R₂ ²A=((X₁₁)²+(X₂₁)²+(X₃₁)²−(X₁₂)²−(X₁₂)²−(X₃₂)²)The spherical coordinates for device 4 disposed on user U_(d) can befound using the above formulas and substituting (x₁, x₂, x₃) for (X₁₄,X₂₄, X₃₄). Additionally, Procedure 2 can be used to determine accordingto the process of the present invention by calculating a direction ofmotion (angle A) toward target T, whereby Angle A is determinedrelatively to the natural coordinates system “North” axis and iscalculated based on the device 4 of mobile user's U_(d) position andtarget coordinates, as follows:cos(A)=(x ₂ −X ₂₄)/R ₄  (16)therefore,A=arcos((x ₂ −X ₂₄)/R ₄)  (17)

Similarly, a direction of motion of user U_(d) of device 4 can becalculated by using one or more of the following steps:

-   -   If Angle A>90 & x₁<X₁₄ then device 4 instructs and or displays        “(180-A) degrees in South-West” direction to user U_(d).    -   If Angle A>90 & x₁>X₁₄ then device 4 instructs and or displays        “(180-A) degrees in South-East” direction to user U_(d).    -   If Angle A<90 & x₁<X₁₄ then device 4 instructs and or displays        “A degrees in North-West” direction to user U_(d).    -   If Angle A<90 & x₁>X₁₄ then device 4 instructs and or displays        “[A] degrees in North-East” direction to user U_(d).

The process of a search consists of the establishing the followingsteps:

-   1. If the distance R₄ to target T exceeds a predetermined threshold    “D”, R₄>D, then monitoring unit notifies user U_(d) of this    condition by displaying <<Search mode>> else <<Monitoring mode>>    (where D—distance threshold).-   2. Otherwise, the monitoring unit notifies user U_(d) that <<Search    mode>> is ON.-   3. Device action DA: Device 4 stores the target ID code to itself    (device 4 of user U_(d)) and sends the target ID code to three    stationary monitoring units devices 1, 2, and 3 of users U_(a),    U_(b) and U_(c), respectively.-   4. Device action of DA for Devices 1, 2, and 3 of users U_(a), U_(b)    and U_(c):    -   a) Device action DA: Devices 1, 2, and 3 of users U_(a), U_(b)        and U_(c) perform a distance measurement to target T identified        by device 4 of user U_(d) in step (3) so as to determine        distances to the target R₁, R₂, and R₃.    -   b) Device action DA: Devices 1, 2, and 3 of users U_(a), U_(b)        and U_(c) transmit or otherwise send back to device 4 of user        U_(d) measured distances to the target R₁, R₂, and R₃, which can        be represented as distance R(i) values, where i is 1-3 having        coordinates values (X₁₁, X₂₁, X₃₁), (X₁₂, X₂₂, X₃₂), (X₁₃, X₂₃,        X₃₃).-   5. Device action DA: Device 4 calculates the target coordinates:    (x₁, x₂, x₃) using P₁ and determines floor location of target T.    -   a) Using P₁ the device 4 calculates the target coordinates: (x₁,        x₂, x₃), which is based on the above information: R₁, R₂, R₃ the        coordinates of mobile devices 1, 2, 3 disposed on users U_(a),        U_(b), U_(c) (X₁₁, X₂₁, X₃₁), (X₁₂, X₂₂, X₃₂), (X₁₃, X₂₃, X₃₃)    -   b) Using P1 the operator 4 device calculates its own coordinates        (X₁₄, X₂₄, X₃₄), and the floor, which is based on distances        between stationary operatiors 1-3 and operator 4: R₁, R₂, R₃ the        coordinates of stationary devices 1, 2, 3 disposed on users        U_(a), U_(b), U_(c) (X₁₁, X₂₁, X₃₁), (X₁₂, X₂₂, X₃₂), (X₁₃, X₂₃,        X₃₃).    -   c) Based on target coordinate x₃ value, the device of device 4        determines the floor location of the target T.-   6. User U_(d) and device 4 can then proceed to another location such    as, for example, to the nearest elevator or stairs.-   7. User U_(d) reaches desired floor, where target T is located.-   8. While user U_(d) is on the desired floor, paragraph 3 is    repeated.-   9. Users U_(a), U_(b) and/or U_(c) repeat step 4.-   10. User U_(d) device 4 repeats paragraph 5.-   11. Based on the (x₁, x₂, x₃) and (X₁₄, X₂₄, X₃₄) coordinate values    of the target T and user U_(d), device 4 can further determine the    direction of motion toward the target A (angle A) using the process    P2 to determine the direction of motion towards the target (angle A    relative to the North Axis) as described above.-   12. If there is an obstacle as user U_(d) moves in a given    direction, U_(d) simply bypasses it and then repeats steps 3-6.-   13. User U_(d) can repeat steps 3-13 until target T is found.

Example (6) Of Three Dimensional Mobile Finding A Single Mobile User andTwo Stationary Users Inside a Building

According to another exemplary example of the method of the presentinvention where a user U_(a) having device 1 is mobile and searching andor tracking a target T inside a building. Two devices 2 and 3 disposedon users U_(b) and U_(c) are located vertically, i.e. one operator isabove other. This method is a derivative method based on the firstexample of finding according to the present invention.

In order to determine the coordinates of the target T; the followingconditions must be satisfied:

-   1. Each of the devices 1, 2 and 3 disposed on users U_(a), U_(b),    and U_(c) so as to establish a system of coordinates in a plane that    is referenced to a coordinate system, for example, four parts of the    world (North-South, East-West). As shown in FIG. 5 devices 2 and 3    disposed on users U_(b) and U_(c) are positioned in such way that    one is above the other.-   2. The total floor height is known or can be estimated, as well as    the height of each floor.-   3. Each of the devices 2 and 3 are configured with their floor and    coordinates.-   4. It is assumed that user Ua is the monitoring master unit that is    searching and or tracking the target T. Device 1 of user Ua is    configured with a compass, altimeter and pedometer or can get the    information such devices provide from another source.-   5. The targets T are equipped with an altimeter.

The following defined terms are used throughout the process description:

R(i)—distance of i-th operator to target,

d—distance traveled (by a particular mobile user)

x₁—first coordinate target T

x₂—second coordinate target T

x₃—third coordinate target T

X₁(i)—first coordinate operator i

X₂(i)—second coordinate operator i

X₃(i)—third coordinate operator i

DA—Device action

Rp(i)—distance between projections of operator (i) and target T.

P(i)—i-th standard computational procedure

RF ID code—target T identification code.

The coordinates of the target T can be calculated Procedure 1 andProcedure 2 can be determined according to the method of the presentinvention where:

Procedure 1 is:R _(pi)=sqr(sqrt(R _(i))−sqrt(X _(3(i)) −X ₃))  (18)Procedure 2: the coordinates calculations for Target is found by:(x ₁ −X ₁₁)²+(x ² −X ₂₁)² =R _(p1) ²  (19)(x ₁ −X ₁₂)²+(x ₂ −X ₂₂)² =R _(p2) ²  (20)(x ₁ −X ₁₃)²+(x ₂ −X ₂₃)² =R _(p3) ²  (21)Remove the parentheses and subtract equation (20) from (19) solutionsfor x₁ and x₂ can be found as follows:x ₁ =A−(B*(D+/−sqrt(D ² −C*E))/C)  (22)x ₂=(D+/−sqrt(D ² −C*E))/C)  (23)whereA=(R_(p1) ²−R_(p2) ²−((X₁₁)²−(X₁₂)²)−((X₂₁)²−(X₂₂)²))/2*(X₁₂−X₁₁)B=(X₂₂−X₂₁)/(X₁₂−X₁₁))C=1+B²D=A*B+X₂₁−B*X₁₁E=A²−2*A*X₁₁+X₂₁ ² +X ₁₁ ²−R_(p1) ².As a result, four points are obtained and are used for consecutivesubstitutions in equation (23). The desired point set of coordinateswill turn equation (23) into equality.Procedure 3: Calculation of searching monitoring device 1 and adirection of motion (angle A) toward target T is determined relativelyto the natural coordinates system “North” axis and is calculated basedon the mobile operator and target coordinates:cos(A)=(x ₂ −X ₂₍₁₎)/R _(p1))  (24)therefore,A=arcos((x ₂ −X ₂₍₁₎)/R_(p1))  (25)user U_(a) having device 1 in the searching and/or can update itsposition by calculating a d value—the distance between the projectionsof the points into the natural coordinate plane and new positions ofuser U_(a) having device 1 (after the user U_(a) moves for a certaindistance, as follows:d=sqr(1−sqrt(X _(3(i))new−X _(3(i))))  (26)Thereafter, four cases are possible according to the number of possibledirections of movement. Accordingly, for every possible direction ofmovement enumerated above, the coordinates of user U_(a) having device 1in the searching and/or after the after the user U_(a) moves for acertain distance in suggested direction.1. X _(1(i)new) =X _(1(i))−sin(A)*d,X _(2(i)new) =X_(2(i))−cos(A)*d  (27)2. X _(1(i)new) =X _(1(i))+sin(A)*d,X _(2(i)new) =X_(2(i))−cos(A)*d  (28)3. X _(1(i)new) =X _(1(i))−sin(A)*d,X _(2(i)new) =X_(2(i))+cos(A)*d  (29)4. X _(1(i)new) =X _(1(i))+sin(A)*d,X _(2(i)new) =X_(2(i))+cos(A)*d  (30)

Similarly, a direction of motion of user U_(a) of device 1 can becalculated by using one or more of the following steps:

-   -   If Angle A>90 & x₁<X₁₍₁₎ then device 1 instructs and or displays        “(180-A) degrees in South-West” direction to user U_(a).    -   If Angle A>90 & x₁>X₁₍₁₎ then device 1 instructs and or displays        “(180-A) degrees in South-East” direction to user U_(a).    -   If Angle A<90 & x₁<X₁₍₁₎ then device 1 instructs and or displays        “A degrees in North-West” direction to user U_(a).    -   If Angle A<90 & x₁>X₁₍₁₎ then device 1 instructs and or displays        “A degrees in North-East” direction to user U_(a).

The process of a search consists of the establishing the followingsteps:

-   -   1. Monitoring device 1 is periodically measuring distance R₁ to        target. If the distance to target exceeds a predetermined        threshold “D”, the device will notify monitoring operator.    -   2. Monitoring device 1 enabled in a search/track mode transmits        the target ID code of the target T to be searched for and/or        tracked, transmits the target ID code of the target T to other        two monitoring devices (device 2 and device 3).    -   3. Monitoring devices 2 and 3 determines the corresponding        distances to the target, i.e. R₂ and R₃, devices 2 and 3 height        values (X₃₂, X₃₃) and devices 2 and 3 coordinates (on the plane)        values (X₂₁, X₂₂), (X₃₁, X₃₂)    -   4. The first monitoring device 1 sends a request to the target T        to read the altimeter value (the target's height).    -   5. Target T device will transmit to first monitoring device the        target “height”, i.e. x₃.        -   a. If the target is on a different floor (X₃₁ is not equal            x₃), user U_(a) of device 1 proceeds to the nearest elevator            or stairs; at the same time device 1 of user U_(a)            determines the direction of the operator movement (angle A            of user U_(a) motion relative to axis “North”). If it is            necessary to change the direction of motion, user U_(a)            calculates the distance traveled and either enters this            value into device 1 or device 1 automatically calculates            this distance based on the user U_(a) request. Thereafter,            user U_(a) enters into device 1 the new direction of motion            and continues to move. From the traveled distance value and            the angle A of user U_(a) motion relative to axis “North”            the operator's device, using procedure P₄, will determine            user U_(a) new coordinates.        -   b. As user U_(a) reaches elevator or stairs and prompts            device 1 to store user U_(a) coordinates before moving in            vertical direction.        -   c. As user U_(a) moves vertically on to desired floor, where            target T is located, user U_(a) device 1 automatically            calculates the floor number    -   6. DA user U_(a) device 1:        -   a. Using procedure P1, user U_(a) device 1 calculates            R_(p1), R_(p2), and R_(p3) based on R₁, R₂, R₃, ((X₁₁),            X₂₁), X₃₁)), ((X₁₂), X₂₂), X₃₂)) and ((X₁₃), X₂₃), X₃₃))            values.        -   b. Using procedure P2, calculates target coordinates (x₁, x₂            on the plane) values based on R_(p1), R_(p2), and R_(p3) and            ((X₁₁), X₂₁), X₃₁)), ((X₁₂), X₂₂), X₃₂)) and ((X₁₃), X₂₃),            X₃₃)) values.        -   c. Using procedure P3, calculates operator 1 direction of            motion (angle A) toward target based on ((X₁₁), X₂₁)), (x₁,            x₂) values. The Angle A, is determined relatively to the            natural coordinates system “North” axis.        -   d. The newly calculated angle A value is stored in the            device.        -   e. Provides graphical prompt to operator.    -   7. User U_(a) device 1 begins movement in a given direction. For        accurate determination of user U_(a) coordinates, user U_(a)        device, after operator moved a certain distance uses procedure        P4 and altimeters readings to update the user U_(a) coordinates.        -   a. Stores user U_(a) updated (new) coordinates values.    -   8. User U_(a) device 1 repeats paragraphs 3-7 until target T is        found.    -   The moment for user U_(a) device 1 coordinates update “operator        moved a certain distance” is calculated when from the following:        sqr(sqrt(X _(11previous) −X _(11new))+sqrt(X _(21previous) −X        _(21new)))>(Predetermined distance)  (31)    -   For example, the predetermined distance value could be set to 10        meters.

Although exemplary embodiments of the present invention have been shownand described with reference to particular embodiments and applicationsthereof, it will be apparent to those having ordinary skill in the artthat a number of changes, modifications, or alterations to the inventionas described herein may be made, none of which depart from the spirit orscope of the present invention. For example, the process can be embodiedin software that resides on some form of electronic device and/orrelated circuitry. The device can be implemented in a circuitry adaptedfor a cellular telephone, a PDA, a portable computer, a two-way radio, aGPS device, a custom electronic device, whereby the devices utilize thesoftware to communicate with each other to determine the location of allof the devices within range of each other and/or the network. All suchchanges, modifications, and alterations should therefore be seen asbeing within the scope of the present invention.

1. An RF system for finding a target T in three dimensional space,comprising: a slave unit disposed on the target T, said slave unitconfigured as a transponder; a monitoring unit configured as atransceiver for monitoring the location of the target T; a wirelesscommunication system, said wireless communication system operating on aRadio Frequency (RF) bandwidth configured to allow communication betweensaid slave and monitoring units, said monitoring unit configured totransmit a ranging signal to said slave unit, said slave unit respondingto said ranging signal by transmitting a reply ranging signal, saidwireless communication system further comprising: a processor fordetermining position information of the target T, said processor incommunication with an antenna, said processor being configured torepeatedly determine values for said position information from: meansfor determining a transmission interval between said monitoring unit andsaid slave unit, said transmission interval being an elapsed timebetween transmitting said ranging signal and receiving said replyranging signal, means for determining a calibration interval betweeneach of said monitoring unit and slave unit said calibration intervalbeing a time interval of a period to normalize the circuitry of saidmonitoring and slave units, and means for determining an antennapropagation interval of said units, said antenna propagation intervalbeing an elapsed time of a signal measured as it passes through saidantenna of said monitoring and slave units, and means for generating ameasured distance between units in three dimensional space, saiddistance generating means determining said measured distance of thetarget T by a spherical virtual triangulation relationship whensuccessive values of said position information has a predeterminedlogical relationship relative to said previous values between saidmonitoring unit and slave unit.
 2. The system according to claim 1,wherein said processor configured to determine said spherical virtualtriangulation relationship based on said position information valuesfrom at least three points P₁, P₂ and P₃ determined for said target Trespective of said monitoring unit, said target T is located utilizingthe point of intersection of at least three circles based on values ofsaid position information relating to said points P₁, P₂ and P₃, wherebysaid points P₁, P₂ and P₃ have circles with radii R₁, R₂ and R₃respective of said monitoring unit to said target T.
 3. The systemaccording to claim 2, wherein said processor is configured to determinesaid spherical virtual triangulation relationship based on measuring thevalue of each of said points P₁, P₂ and P₃ not in a straight linerelative to said monitoring unit to reduce ambiguity, each measurementof the value of said radii R₁, R₂ and or R₃ to pinpoint the target Tutilizing a position of said monitoring unit.
 4. A method for finding atarget in three dimensional space, comprising the steps of: determiningthree spheres between successive readings between one of a transponderdisposed on the target T and a transceiver each operating using radiofrequency (RF), said spheres determined by successive readings eachhaving centers that do not lie on one straight line; numbering threeseparate points of an intersection of said spheres as equal either tozero or one, or two; and calculating a position of the target T from theinformation of said number of points.